If the 1099-R IRA gross distribution (box 1) is the same as the taxable amount (box2a), but our known cost basis indicates less, how to enter correct taxable amount?

You don't enter the taxable amount. You enter the basis and other information. TurboTax will then calculate the taxable amount.

Enter the 1099-R as-is. After you enter the 1099-R, and after the summary screen "Your 1099-R Entries," continue through the questions. You will come to a screen that asks if you made any nondeductible contributions to your IRA. Answer Yes. On the next screen you will be able to enter the basis. Continue and answer the follow-up questions.

If you made nondeductible IRA contributions in previous years you should have reported them on Form 8606 each year. Then you would take the basis from the most recent Form 8606.